# The competition I entered into the first MathsJam Competition Competition

A couple of weekends ago was the big MathsJam gathering (I might call it a recreational maths conference, but this is discouraged). Two of the delightful sideshows, alongside an excellent series of talks, were the competitions. The Baking Competition is fairly straightforward, with prizes for “best flavour, best presentation, and best maths”:

The first will reward a well-made, delicious item; the second will reward the item which has been decorated the most beautifully and looks most like what it’s supposed to be; and the third will reward the most ingenious mathematical theming.

You can view the entries from this year on the MathsJam website.

The other regular competition is the Competition Competition. This invites attendees to submit a competition, which other attendees can enter. There are some rules, including minimum font size, paper size and maximum value of prize. To be clear, the rules say “any type of competition is permitted as long as it can be judged by the setter (or a winner randomly chosen from the correct entries)”.

Prizes are awarded for best competition, popular vote winner (the competition with the most entries) and “best attempt at circumvention of the rules while still strictly sticking to the rules”. Seeing people attempt the latter is quite delightful.

Chatting to people at MathsJam this year, I was reminded of my entry into the Competition Competition when it first ran in 2014. I invited entrants to write down an integer between 0 and 100, then I said that I would run a Shapiro-Wilk test of normality on the numbers people had written down. This tests the null hypothesis that the data come from a normally distributed population. The competitive element of the competition asked people to guess the p-value obtained from that test.

While we were chatting about this, The Aperiodical’s own Paul Taylor asked me what p-value came out as. I couldn’t remember, but I’ve looked it up. The numbers entered were as follows:

Number entered Number of people entering it
2 1
6 1
12 1
16 1
50 1
71 1
72 2
73 2
86 2
97 2
99 7

In a sample of 21 integers from 1-99 where only four numbers are below 50 and one third are precisely 99, it may not surprise you to learn that the statistical test gave strong evidence to reject the hypothesis that these data were from a normally distributed population. The p-value (from R) was 0.0002211865 and the winner was Francis Hunt, who guessed 0.0001.

You can find out about the MathsJam competitions and other side activities that take place on the MathsJam Extras page.